Answer to Question #185867 in Discrete Mathematics for Richard Kelly

Question

1.     Suppose that f is defined recursively by:

     f (0) 5= and f n( + =1) 2fn+5. Find f(1), f(2), f(3) and f(4)? 

Answer 1

We have given that,

$f(0) = 5$

$f(n+1) = 2f(n)+5$

Putting, $n=0$

$f(1) = 2f(0)+5 = 2 \times 5+5 = 15$

Putting, $n = 1$

$f(2) = 2f(1)+5 = 2 \times 15 +5 = 35$

Putting, $n=2$

$f(3) = 2f(2)+5 = 2 \times 35+5 = 75$

Putting $n = 3$

$f(4) = 2f(3)+5 = 2 \times 75 +5 = 155$